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in Mathematics by (72.7k points)

An unbiased die, with faces numbered 1,2,3, 4, 5, 6, is thrown n times and the list of n numbers showing up is noted. What is the probability that among the numbers 1, 2, 3, 4, 5, 6 only three numbers appear in this list?

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Let us define a onto function F from A : [r1,r2 ... rn] to B: [1, 2,3] where r1, r2, . , rn, are the readings of n throws and 1, 2, 3 are the numbers that appear in the n throws. 

Number of such functions, M = N - [n(1) -n(z)+ n(3)] 

where N = total number of functions and n(t) = number of function having exactly t elements in the range.

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